Problem: Simplify the following expression: $\dfrac{36t^2}{60t}$ You can assume $t \neq 0$.
Solution: $ \dfrac{36t^2}{60t} = \dfrac{36}{60} \cdot \dfrac{t^2}{t} $ To simplify $\frac{36}{60}$ , find the greatest common factor (GCD) of $36$ and $60$ $36 = 2 \cdot 2 \cdot 3 \cdot 3$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(36, 60) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{36}{60} \cdot \dfrac{t^2}{t} = \dfrac{12 \cdot 3}{12 \cdot 5} \cdot \dfrac{t^2}{t} $ $\phantom{ \dfrac{36}{60} \cdot \dfrac{2}{1}} = \dfrac{3}{5} \cdot \dfrac{t^2}{t} $ $ \dfrac{t^2}{t} = \dfrac{t \cdot t}{t} = t $ $ \dfrac{3}{5} \cdot t = \dfrac{3t}{5} $